This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants.
The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed.
The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book.
The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem.
This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants.
The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed.
The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem.
Due to its very clear style and the careful organization of the material, this truly brilliant book may serve as an introduction into the field, yet it also provides an excellent source of information on specific topics in spectral theory for the working mathematician.
Review of the first edition by M. Grosser, Vienna
Monatshefte für Mathematik Vol. 146, No. 1/2005
Rezensionen / Stimmen
From the reviews of the second edition:
"This is a nicely written and useful book. It is to a large extent self-contained, so that it can be read . not only by specialists and by Ph. D. students specializing in operator theory, but also by university students of higher courses, who are familiar with basic facts on Banach spaces." (Wieslaw Tadeusz Zelazko, Zentralblatt MATH, Vol. 1208, 2011)
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ISBN-13
978-3-7643-8265-0 (9783764382650)
DOI
10.1007/978-3-7643-8265-0
Schweitzer Klassifikation
Banach Algebras.- Operators.- Essential Spectrum.- Taylor Spectrum.- Orbits and Capacity.
